The federation was suspended in November 2015 following a report commissioned by the World Anti-Doping Agency (WADA) that found evidence of systematic, state-sponsored doping in the sport.
Federation spokeswoman Natalia Yukhareva told Reuters it had filed an appeal with CAS against the IAAF's decision to extend the federation's suspension at its last council meeting in July.
At the time the IAAF said that Russia had made "significant progress" in meeting criteria for reinstatement, but that its suspension would remain in place until the council convened again in December.
CAS did not immediately return a request for comment.
The move comes days after WADA conditionally reinstated Russian anti-doping agency RUSADA, angering sports bodies around the globe.
The IAAF -- which said on Wednesday it was set on "robustly defending any challenge" to the suspension of the Russian athletics federation -- said last week that RUSADA's reinstatement fulfilled one of three pre-conditions for the federation's return to its fold.
For the federation to be reinstated, Russia must acknowledge that officials from the Sports Ministry were involved in doping cover-up schemes. Russian authorities must also provide access to data from testing samples at the Moscow lab, which was also suspended in the wake of the 2015 scandal.
While Russia has pledged to cooperate with global sports bodies to curb the use of banned performance-enhancing drugs, the authorities have vehemently denied the existence of state-sponsored doping in the country.
"The IAAF has, from the very beginning, been clear on its reinstatement requirements and processes overseen by an independent Taskforce," the IAAF said in a statement. "We stand behind the decisions we have made and are very confident of our legal position."
The IAAF added it that the federation can only be reinstated "by satisfying the reinstatement conditions to the satisfaction of the IAAF Council."
The Taskforce will report back at the next IAAF Council meeting in Monaco in December.
The president of Russia's athletics federation, Dmitry Shlyakhtin, said the appeal was aimed at having the requirements removed from its reinstatement criteria.
"In our view it is unjustified (to require) compliance with these criteria and their presence on the roadmap for reinstating the federation is illegitimate because they lie beyond its competence," Shlyakhtin said in a statement.
Despite the federation's suspension, a string of Russian athletes, including 2015 world champion hurdler Sergey Shubenkov, have been cleared to compete internationally after demonstrating they are training in a doping-free environment.
(Reporting by Gabrielle Tétrault-Farber, additional reporting by Mitch Phillips, Editing by Christian Radnedge)
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